An Algorithm for Solving Linear Optimization Problems Subjected to the Intersection of Two Fuzzy Relational Inequalities Defined by Frank Family of T-Norms
A. Ghodousian*. International Journal in Foundations of Computer Science & Technology ( IJFCST ), 18 (3):
20(May 2018)
Abstract
Frank t-norms are parametric family of continuous Archimedean t-norms whose members are also strict functions. Very often, this family of t-norms is also called the family of fundamental t-norms because of the role it plays in several applications. In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated. The feasible region is formed as the intersection of two inequality fuzzy systems defined by frank family of t-norms is considered as fuzzy composition. First, the resolution of the feasible solutions set is studied where the two fuzzy inequality systems are defined with max-Frank composition. Second, some related basic and theoretical properties are derived. Then, a necessary and sufficient condition and three other necessary conditions are presented to conceptualize the
feasibility of the problem. Subsequently, it is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. Finally, an algorithm is presented to solve the problem and an example is described to illustrate the algorithm. Additionally, a method is proposed to generate random feasible max-Frank fuzzy relational inequalities. By this method, we can easily generate a feasible test problem and employ our algorithm to it.
%0 Journal Article
%1 noauthororeditor
%A Ghodousian*, Amin
%D 2018
%J International Journal in Foundations of Computer Science & Technology ( IJFCST )
%K Fuzzy compositions fuzzy inequality linear optimization relation relational t-norms.
%N 3
%P 20
%T An Algorithm for Solving Linear Optimization Problems Subjected to the Intersection of Two Fuzzy Relational Inequalities Defined by Frank Family of T-Norms
%U https://wireilla.com/papers/ijfcst/V8N3/8318ijfcst01.pdf
%V 18
%X Frank t-norms are parametric family of continuous Archimedean t-norms whose members are also strict functions. Very often, this family of t-norms is also called the family of fundamental t-norms because of the role it plays in several applications. In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated. The feasible region is formed as the intersection of two inequality fuzzy systems defined by frank family of t-norms is considered as fuzzy composition. First, the resolution of the feasible solutions set is studied where the two fuzzy inequality systems are defined with max-Frank composition. Second, some related basic and theoretical properties are derived. Then, a necessary and sufficient condition and three other necessary conditions are presented to conceptualize the
feasibility of the problem. Subsequently, it is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. Finally, an algorithm is presented to solve the problem and an example is described to illustrate the algorithm. Additionally, a method is proposed to generate random feasible max-Frank fuzzy relational inequalities. By this method, we can easily generate a feasible test problem and employ our algorithm to it.
@article{noauthororeditor,
abstract = {Frank t-norms are parametric family of continuous Archimedean t-norms whose members are also strict functions. Very often, this family of t-norms is also called the family of fundamental t-norms because of the role it plays in several applications. In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated. The feasible region is formed as the intersection of two inequality fuzzy systems defined by frank family of t-norms is considered as fuzzy composition. First, the resolution of the feasible solutions set is studied where the two fuzzy inequality systems are defined with max-Frank composition. Second, some related basic and theoretical properties are derived. Then, a necessary and sufficient condition and three other necessary conditions are presented to conceptualize the
feasibility of the problem. Subsequently, it is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. Finally, an algorithm is presented to solve the problem and an example is described to illustrate the algorithm. Additionally, a method is proposed to generate random feasible max-Frank fuzzy relational inequalities. By this method, we can easily generate a feasible test problem and employ our algorithm to it.
},
added-at = {2022-10-14T11:34:29.000+0200},
author = {Ghodousian*, Amin},
biburl = {https://www.bibsonomy.org/bibtex/28d31b232c5e84725912f07412018e2f8/devino},
interhash = {6f1a50ea6545fd0df04ecf2f4b241194},
intrahash = {8d31b232c5e84725912f07412018e2f8},
journal = { International Journal in Foundations of Computer Science & Technology ( IJFCST )},
keywords = {Fuzzy compositions fuzzy inequality linear optimization relation relational t-norms.},
month = may,
number = 3,
pages = 20,
timestamp = {2022-10-14T11:34:29.000+0200},
title = {An Algorithm for Solving Linear Optimization Problems Subjected to the Intersection of Two Fuzzy Relational Inequalities Defined by Frank Family of T-Norms
},
url = {https://wireilla.com/papers/ijfcst/V8N3/8318ijfcst01.pdf},
volume = 18,
year = 2018
}